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<font color="Maroon" title="c4">f</font> <a href="mesfunc6.html#R3" title="MESFUNC6:pred.3">is_integrable_on</a>  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="random_1.html#D3" target="_self" title="RANDOM_1:def.3">Def3</a></span>;<br/>
<a NAME="E2:47_1_1"/><span class="kw">then </span>
(  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font></span>)</span>,<font color="Maroon" title="c4">f</font>) &amp;  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font></span>)</span>,<font color="Maroon" title="c4">f</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc6.html#T90" title="MESFUNC6:th.90">MESFUNC6:90</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:47_1_1"/>
 <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font></span>)</span>,<font color="Maroon" title="c4">f</font>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T48" title="XXREAL_0:th.48">XXREAL_0:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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